The coalition battle over constitutional reform has intensified after Vince Cable, the business secretary, said he was confident that in alliance with Labour his party could defeat any attempt by David Cameron to force through parliamentary boundary changes next year.

He also broadened Liberal Democrat opposition to the reforms, saying they were unpopular with constituents who did not want to see local communities disrupted.

Nick Clegg, the Lib Dem leader said on Monday that he would be instructing his MPs to vote against the boundary reforms in revenge for Cameron being unable to coerce his MPs to back plans for a largely elected house of Lords.

Cameron has said he will still try to force the boundary reviews through the Commons and Lords next year, saying the idea of equally sized constituencies was a long-standing demand of the Chartists, the radical movement for working class emancipation in the mid-19th centrury. He intends to embarrass the Liberal Democrats by pointing out that his reforms, likely to benefit the Conservatives at the 2015 election, are also designed to cut the size of parliament to 600 MPs, which would also cut the cost of politics.

Speaking to his local paper, the Richmond and Twickenham Times, Cable said: "We've taken the view that if we can't get the support of the Conservatives to pursue House of Lords reform we don't see why we should support constitutional change, which they are very anxious to have.

"Obviously if there's a vote then there's a vote, but I think the Conservatives alone don't have enough. There are a lot of Conservatives themselves who are unhappy with the boundary changes, but even if they all voted for the changes there are not enough votes to get it through.

"I will be 100% supporting Nick Clegg's suggestion. We maintain complete solidarity on this issue."

Cable said the proposals threatened to disrupt voters' sense of identity.

He said: "The impression I have is that those people in my constituency prefer to keep the boundaries as they are. They don't want to be hacked up and be combined with bits of Hounslow and lose bits of their identity.

"The Liberal Democrats have made it very clear we will be opposing changes and I think Labour will be opposing the changes, so I think it's very difficult to say they will proceed.

"I think essentially the likely outcome now is the status quo. I think most people would prefer that, and it makes life easier in terms of campaigning for both of the borough's sitting MPs because we are campaigning in areas we know and where people voted for and against in the past.

The business secretary set out his position as Stewart Jackson, the Conservative MP for Peterborough, said it would be untenable for Lib Dem ministers to vote against government policy and remain in office, adding it would be weak of David Cameron to allow this to happen.